Social psychologists Philip Mazzocco and Mahzarin Banaji once asked white volunteers how much money would cover the “costs” of being born black instead of white. The volunteers guessed that about $5,000 ought to cover the lifetime disadvantages of being an average black person rather than an average white person, in the United States. By contrast, when asked how much they wanted to go without television, the volunteers demanded a million dollars.

Mazzocco and Banaji were taken aback: The average black person in America is 447 percent more likely to be imprisoned than the average white person, and 521 percent more likely to be murdered. Blacks earn 60 cents to the dollar compared with whites who have the same education levels and marital status. The black poverty rate is nearly twice the white poverty rate. Blacks tend to die five years earlier than whites; the infant mortality rate among black babies is nearly 1 1/2 times the rate among white babies. And because of long-standing patterns of inheritance, blacks and whites begin life with substantial disparities in family wealth.

“The point we were making is, whatever the cost of being black might be, whites are vastly underestimating it,” said Mazzocco, of Ohio State University at Mansfield. “You throw in the 5-to-1 wealth gap . . . if you wanted to put a dollar-and-cents value on the difference, you would come up with a number much larger than $5,000.”

The unusual experiment is one of dozens that have found that whites tend to have a relatively rosy impression of what it means to be a black person in America. Whites are more than twice as likely as blacks to believe that the position of African Americans has improved a great deal. Blacks are more than twice as likely as whites to believe that conditions for African Americans are growing worse.

This long-standing war of perceptions created the perfect storm last week after sermons by the Rev. Jeremiah Wright — former pastor of Sen. Barack Obama (D-Ill.) — painted a picture of stark inequality at odds with white perceptions.

Mazzocco and Banaji, who teaches at Harvard, found that when volunteers learned about the disparities, they started to demand much larger sums of money.

“Many whites assume blacks are making use of old crimes to gain present-day benefits that are unearned,” Mazzocco said. “Underlying this is a misunderstanding and ignorance about black costs and white privilege.”

But knowledge about disparities is not the only reason whites and blacks have different perceptions about racial equality. Social psychologist Richard Eibach at Yale University has shown that whites and blacks often employ different yardsticks to measure racial equality. Whites tend to measure progress by comparing the present and the past — and America has made giant strides since the Jim Crow era. Nonwhites, Eibach found, are likely to evaluate racial equality in comparison with an idealized future. These yardsticks create entirely different perceptions.

When Eibach asked each group to use the other’s yardstick — whites to focus on the future and nonwhites to think about the past — the differences disappeared. Now, everyone agreed the country had come a long way — and had a long way to go.